The Low-Mass End of the 𝑀_BH/𝑀_host Relation in Quasars

Abstract

The 𝑀_BH-𝑀_host relation in quasars has been probed only in a limited parameter space, namely, at 𝑀_BH∼10⁹ M_⊙ and 𝑀_host∼10¹²  M_⊙. Here we present a study of 26 quasars laying in the low-mass end of the relation, down to 𝑀_BH∼10⁷ M_⊙. We selected quasars from the SDSS and HST-FOS archives, requiring modest 𝑀_BH (as derived through the virial paradigm). We imaged our sources in 𝐻 band from the Nordic Optical Telescope. The quasar host galaxies have been resolved in 25 out of 26 observed targets. Host galaxy luminosities and stellar masses are computed, under reasonable assumptions on their star formation histories. Combining these results with those from our previous studies, we manage to extend the sampled parameter space of the 𝑀_BH-𝑀_host relation in quasars. The relation holds over 2 dex in both the parameters. For the first time, we are able to measure the slope of the 𝑀_BH-𝑀_host relation in quasars. We find that it is consistent with the linear case (similarly to what observed in quiescent galaxies). We do not find any evidence of a population of massive black holes lying below the relation.

1. Introduction

Massive black holes (BHs) are ubiquitously found in the centre of massive galaxies [1–3]. Their masses (𝑀_BH) show strong correlations with large-scale properties of the host galaxies, namely, the stellar velocity dispersion (𝜎_∗, [4–7]), the luminosity, and mass of the spheroidal component (𝐿_host, 𝑀_host; see [8–10]). These relations have been interpreted as the outcome of a joint evolution between BHs and their host galaxies [11–18]. In this scenario, the growth of BHs through accretion regulates the gas cooling in the outskirt of host galaxies through energy or momentum injection (feedback), thus quenching the formation of stars. Galaxy mergers may also play a role in this scenario, as gravitationally induced dynamical instabilities may trigger both star formation bursts and gas inflows fuelling the BH activity ([12, 19–21], see also [22]).

The 𝑀_BH-host galaxy relations have been pinned down on an albeit small set of local, mostly quiescent galaxies. The sampled parameter space ranges over 3 dex in masses, from a few million to a few billion solar masses in terms of 𝑀_BH. Extending these studies beyond the local Universe is challenging. On one side, the influence radius of BHs, 𝑅_inf, that is, the radius where the gravitational potential is dominated by the singularity, is resolved only in very nearby objects (distances < few tens Mpc) with high 𝑀_BH values. For any other sources, indirect tracers of 𝑀_BH are required. The most commonly adopted indirect estimator of 𝑀_BH is based on the width of broad emission lines and the size of the broad line region (BLR). This can be done only in type-1 AGN, where broad lines are observed [23–26]. This approach allows to estimate 𝑀_BH from single-epoch spectra in ~100 000 quasars up to 𝑧∼5 from SDSS spectra [27], and in most of the 𝑧∼6 quasars known to day [28–31]. (Caveats to this technique arise as BLR clouds may be supported by radiation pressure [32] or move nonvirially; projection effects depending on the geometry and orientation of the BLR may hinder our ability to actually measure the orbital velocity of clouds [33, 34]; different emission lines may be produced in regions where the gas dynamics are different [35–39].)

On the other side, the properties of host galaxies are hard to measure in distant sources. Bright active nuclei (necessary to measure 𝑀_BH) can easily outshine the light of their host galaxies. Observations in excellent seeing conditions (e.g., [40, 41])or based on adaptive optics (e.g., [42, 43]) are required. Diffraction-limited observations with HST have also significantly contributed in this field [44–54], although some concerns about the reproducibility of the PSF have been arisen [51]. Up to now, ∼300 quasar host galaxies have been resolved up to 𝑧≈3, and most of them at 𝑧<0.5 (see [40], and references therein).

In order to understand the processes and timescales which led to the onset of the BH-host galaxy relations, two key observational tests are required. The first one consists in tracing the evolution of the BH-to-host galaxy mass ratio ( Γ≡𝑀_BH/𝑀_host) as a function of Cosmic Time. If, for example, Γ(𝑧>0)<Γ(𝑧≈0), then we can argue that the BHs in these systems still have to accrete in already formed bulges. Vice versa, Γ(𝑧>0)>Γ(𝑧≈0) could suggest a rapid growth of the BHs, followed by a slower build-up of the spheroids. Most of the studies on the evolution of the BH-host galaxy relations suggest that at high redshift, for a given mass of the host spheroid, the harbored BH is more massive than at low-𝑧 [50, 53, 55–58], with Γ(𝑧)∝(1+𝑧)^3/2. It is interesting to note that the host galaxy of J1148 + 5251, the highest-𝑧 SDSS quasar, at 𝑧=6.42, shows an 𝑀_BH-host galaxy dynamical mass ratio of ≈0.13 [59, 60], in an order-of-magnitude agreement with the extrapolation from the 𝑧<3 studies.

A second observational test to probe the onset of the BH-host galaxy relations is to trace the low-mass end of the BH-host galaxy relations. Different initial host galaxy mass, BH seed mass, and build-up processes produce different slopes of the relations, especially at low mass. Light seeds (10−100M_⊙) are expected as the remnants of metal-pure stars in the early Universe, while heavier seeds (up to ∼10⁵M_⊙) can result from the direct collapse of primordial gas clouds. The former ones would produce a larger scatter in the 𝑀_BH-host relations, a higher occupation fration in relatively small galaxies, and a lower cutoff in the minimum 𝑀_BH with respect to the latter (see, e.g., [61], and references therein). Some authors even claim that the 𝑀_BH−𝜎_∗ relation itself is just the upper limit of a broader distribution, with a number of (hard-to-detect) modest-mass BHs embedded in relatively massive galaxies (e.g., [62]).

The low-mass end of the 𝑀_BH-host galaxy relations has been probed down to few 10⁵𝑀_BH in quiescent galaxies or in low-luminosity AGN at low-𝑧 [54, 63–67], suggesting that the 𝑀_BH-host relations hold in quiescent or mildly active galaxies. However, no effort has been attempted so far to extend this test to higher luminosity AGN. Quasars are ideal probes of the BH-host galaxy relations at 𝑧>0. However, while Γ in quasars has been measured up to very high redshift, the ranges of 𝑀_BH and 𝑀_host investigated up to date are limited, and comparable with the observed scatter of the BH-host galaxy relations. Filling the low-mass end of the 𝑀_BH-𝑀_host relation therefore represents a main challenge and a fundamental step in our comprehension of the BH-host galaxy evolution. In this paper, we present ground-based NIR observations of quasars at 𝑧<0.5 selected so that virial 𝑀_BH<10⁹𝑀_BH. Our imaging campaign successfully resolved 25 quasar host galaxies. This enables us to directly probe the slope of the 𝑀_BH-𝑀_host relation in quasars.

The structure of this work is the following: in Section 2 we describe the sample. In Section 3 we present the analysis of the spectra and we derive 𝑀_BH in all our sources. The new observations, the data reduction and analysis, and the results from the imaging campaign are presented in Section 4. In Section 5 we discuss our results. Conclusions are summarized in Section 6. Throughout the paper we will assume a standard cosmology with 𝐻₀=70kms⁻¹ Mpc⁻¹, Ω_m=0.3, and Ω_Λ=0.7.

2. The Sample

We selected quasars at 𝑧<0.5 with available H𝛽 observations in the Sloan Digital Sky Survey (SDSS [68]) spectroscopic database or C_IV or Mg_II observations in the HST-Faint Object Spectrograph (FOS) archive. We require that black hole virial masses, computed as described in Section 3, range between 10⁷ and 10⁹ M_⊙. Note that, out of the 62 𝑧<0.5 quasars examined in our previous study [26], only 8 (13%) had 𝑀_BH<10⁹M_⊙. We then selected quasars having at least 3 relatively bright (𝑚_𝐻=10−15 mag) stars within 2′ (corresponding to the half size of the NOTCam field of view), and a number of fainter stars in order to have an accurate description of the Point Spread Function (PSF). Observability constraints and modest weather losses further limited our analysis to 26 targets (see Table 1), mostly detected in radio wavelengths according to the [69] catalogue. This new sample is then matched with the 62 𝑧<0.5 targets presented in our previous study of the 𝑀_BH-𝑀_host relation [26, 58]. Figure 1 compares the distribution of 𝑀_BH in the general SDSS sample at 𝑧<0.5, computed from the continuum luminosities and H𝛽 width estimates reported by [27], with the ones presented in [26] and in the present study.

Table 1 

The sample. (1) Target name. (2-3) Right ascension and declination (J2000). (4) Is the target detected in radio wavelengths, according to the [69] catalogue? (5) Catalogue redshift. (6) Apparent visual magnitude of the quasar.

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(b)

(c)

Figure 1 

Comparison among the 𝑀BH distributions in the SDSS quasars at 𝑧<0.5 [27] (a), in our 2010 study (b) and in the present work (c). The latter is clearly more representative of the general quasar population at low redshift.

3. The Spectroscopic Dataset

The spectroscopic dataset consists of pipeline-processed, publicly available spectra from the SDSS or FOS archive. SDSS spectra have 𝜆/Δ𝜆∼2000 and a spectral range between 3800 and 9000 Å. Uncertainties on wavelength calibration amount to 0.05 Å, while flux calibration formal errors account to 5%. FOS spectra are taken from the compilation of recalibrated quasar and AGN FOS spectra by [70]. Observations were performed with a number of different gratings at both high spectral resolution (1–6 Å diode⁻¹, 𝜆/Δ𝜆≈1300) and low spectral resolution (6–25 Å diode⁻¹, 𝜆/Δ𝜆≈250) covering various spectral windows from 1140 Å to 3275 Å. Photometric uncertainties are usually 5–10%, while typical wavelength calibration uncertainties are around 0.5 channels rms (see [70]).

Spectral analysis follows the same approach described in [26] and [31]. Briefly, continua are modeled as a superposition of a power-law component, the host galaxy emission (only in the optical spectra; the Elliptical model by [71] was adopted as a template), and the Fe_II multiplets (modeled on the template by [72]). Relevant broad emission lines (H𝛽, Mg_II, and C_IV) are modeled with the superposition of two Gaussian curves with the same peak wavelength. The spectral resolution of the SDSS data is adequate to allow an easy identification of the narrow H𝛽 emission with respect to the broad line. Examples of the line fitting are shown in Figure 2.

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(b)

Figure 2 

Examples of H𝛽 line fitting. The observed spectra, shifted to the rest frame, are plotted in solid, black lines. The various components of the models are shown: the power-law (black, dotted line), the host galaxy and FeII templates (green, solid line), the line model (red, solid line), and its components (red, dotted lines). Fit residuals are shown in blue, dashed lines.

We measure the continuum luminosity at 1350, 3000, and 5100 Å from the fitted power-law. The broad line luminosity and FWHM are measured from the line model (see [36], for a discussion on the fitting technique and the parametrization of the relevant quantities). Virial black hole masses are computed with the same recipes used in [26], adopting geometrical factors of 1.6 for H𝛽 and Mg_II and 2.4 for C_IV. Table 2 lists the main measurements and inferred quantities from the spectroscopic analysis. (We note that, after a careful reanalysis of the spectra, two objects (B20110+29 and B20752+25𝐴) show values of 𝑀_BH slightly exceeding the initial selection criteria. Nevertheless, we include these sources in the present analysis.)

Table 2 

Results from the spectroscopic analysis. (1) Quasar name. (2) Redshift. (3) Line used in the 𝑀_𝐵𝐻 estimate. (4) Continuum monochromatic luminosity at 1350 (for C_IV), 3000 (for Mg_II) or 5100 Å (for H𝛽), in ergs⁻¹. (5) Line FWHM in km s⁻¹. (6) Virial estimate of the black hole mass, in solar units.

4. The Imaging Dataset

All the objects in our study have been observed in 𝐻 band in a campaign at the 2.5 m Nordic Optical Telescope (Roque de Los Muchachos, Spain) using NOTCam. Observations were carried out during three observing runs in May 2007 and April and November 2008. The average seeing in 𝐻 band was 0.7^”. The 1024×1024 pixel NOTCam detector has a pixel scale of 0.235^” pxl⁻¹, yielding a field of view size of ∼4×4 arcmin². Usual observing techniques for broad-band NIR imaging of point-like sources were adopted. Observations were split in 1 min long individual frames. Random jittering patterns within a 20^” box were adopted in order to perform optimal sky subtraction. The total time on each source was 45 min.

Data reduction was performed using IRAF. (IRAF is distributed by the National Optical Astronomy Observatories, which are operated by the Association of Universities for Research in Astronomy, Inc., under cooperative agreement with the National Science Foundation.) Bad pixels were corrected for in each image using a mask made from the ratio of two sky flats with different illumination levels. Sky subtraction was performed for each science image using a median averaged frame of all the other temporally close frames in a grid of eight exposures. Flat fielding was made using normalized median averaged twilight sky frames with different illumination levels. Finally, images were aligned to subpixel accuracy using field stars as reference points and combined after removing spurious pixel values to obtain the final reduced coadded image. Zero point calibration is achieved by cross-matching the photometry of field stars with the 2MASS database. This approach yields typical photometric uncertainties <0.1 mag.

We analyzed our data using the Astronomical Image Decomposition and Analysis package (AIDA; [73]), an IDL-based software designed to perform two-dimensional model fitting of quasar images. Details on the procedure are presented in [40, 74] and briefly summarized here.

A careful modeling of the Point Spread Function (PSF) is crucial to disentangle the extended host galaxy light from the nuclear source. To model the PSF shape, we used suitable field stars. Each star was modeled with four two-dimensional Gaussians, representing the core of the PSF, and an exponential feature, representing the extended wing of the PSF. Regions contaminated by nearby sources, saturated pixels, and other defects affecting the images were masked out.

In order to discriminate between resolved and unresolved targets, we first fit the images of our sources with the pure PSF model. In most of the cases, an extended halo was clearly observed in the residuals. We then reperformed the fits using a Sersic law, (describing the host galaxy) plus a point-source (the nucleus), convolved to the PSF model. In all but one case (J02331−0909), this second fit is significantly better than the fit with the pure PSF, as confirmed by the 𝜒² ratio between the two fits (see Table 3).

Table 3 

Results from the imaging analysis. (1) Quasar name. (2) Redshift. (3) Apparent observed 𝐻-band magnitude of the nucleus. (4) Apparent observed 𝐻-band magnitude of the host galaxy. (5) Apparent central surface brightness, as extrapolated from the host galaxy model. (6) Chi-square ratio between the best fit using a pure PSF and the best fit using a galaxy+quasar model. (7) Effective radius of the host galaxy. (8) Ellipticity of the host galaxy model. (9) Sersic index of the host galaxy model. (10) Rest-frame 𝑅-observed 𝐻 color correction. (11) Resulting absolute rest-frame 𝑅-band magnitude of the host galaxy. (12) Adopted mass-to-light ratio. (13) Stellar mass of the host galaxy. (14) BH-to-host galaxy mass ratio.

An example of the outputs of our analysis is shown in Figure 3.

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(b)

(c)

(d)

(e)

(f)

(g)

(h)

(i)

(j)

(k)

(l)

Figure 3 

An example of the analysis of the quasar host galaxies, shown in the case of the quasar J08285+2748. Top panels: observed quasar image (left), contour plot (center), and light profile (right; the PSF and galaxy models are plotted in dotted and dashed lines, resp.). Central panels: similarly, the images (left), contour plots (center), and light profile (right) of the PSF and the galaxy model. Bottom panels: image (left), contour plot (center), and light profile (top right) of residuals after model subtraction. The radial distribution of 𝜒2 values is also plotted (bottom right).

Host galaxy apparent 𝐻-band magnitudes are then converted into rest-frame 𝑅-band. We use the Elliptical galaxy template by [71] to estimate 𝑘-corrections. The host galaxy 𝑅-band absolute magnitude is then converted into a stellar mass by adopting the mass-to-light ratio (𝑀/𝐿) of a single stellar population originated at 𝑧_burst=5 and passively evolving down to 𝑧=0 (see [58], for details). Table 3 summarizes the relevant results from the modeling of the quasar host galaxies described here.

5. Discussion

In Figure 4 we show the 𝑀_BH-𝑀_host relation for quasar host galaxies at 𝑧<0.5. The dataset (62 objects from [26, 58], plus 25 objects with resolved host galaxies from the present study) span over 2 dex in both 𝑀_BH and 𝑀_host. The same 𝑀_BH-𝑀_host relation observed for inactive galaxies appears to hold through all the sampled range, from ∼3×10¹⁰ to ∼3×10¹²M_⊙ in terms of 𝑀_host. We find that ⟨logΓ⟩=−2.843 (in excellent agreement with the 𝑀_BH=0.0015𝑀_host value reported by [9], for inactive galaxies) with a 0.44 dex scatter. Only 3 sources (J02321+0008, PG1404+226 from this study; 1001+291 from the old sample) lie more than 2-𝜎  below the relation. Since the sampled parameter space is about 5 times larger than the dispersion of the relation, we can exclude that the observed 𝑀_BH-𝑀_host relation is the upper envelope of a population of quasars with relatively small black holes hosted by very massive galaxies. The best bilinear regression fit of the relation is𝑀log^BH10⁹M_⊙=()𝑀1.26±0.29×log^host7⋅10¹¹M_⊙+(0.04±0.03), (1) consistent with the relations with a constant 𝑀_BH/𝑀_host ratio, as observed in quiescent galaxies in the local Universe [9, 10].

Figure 4 

The 𝑀BH-𝑀host relation in the objects in our sample (filled symbols), as compared with the 𝑧<0.5 sample from [58] (empty symbols) and the local relation (𝑀BH/𝑀host=0.0015; see [9]). Squares, triangles, and circles refer to 𝑀BH estimates derived from H𝛽, MgII, and CIV respectively. Our new data substantially extend the sampled range of the 𝑀BH-𝑀host relation. The relation holds down to quasar host masses of ∼1011M⊙ (BH masses of ∼108M⊙). There is no evidence of a population of objects lying below the relation, as claimed by [62]. The overall scatter of the 𝑀BH-𝑀host relation is 0.44 dex, and it extends over 2 dex both in terms of host galaxy and BH mass. Dotted, horizontal lines show how our objects would move if the correction for the bulge-to-total luminosity ratio is taken into account (see the text for details). The solid line is the best fit to our data.

When considering subsets of our data, the high-mass end shows a slightly smaller scatter (see Table 4).

Table 4 

Average values of the 𝑀_BH/𝑀_host ratio in various subsets of our sample. (1) Subsample. (2) Number of objects. (3) Average value of log Γ. (4) Root Mean Square of log Γ.

For twelve objects the host galaxies are found to be best described by a Sersic law with small index (𝑛_s<1.5), suggesting the presence of significant disc components. In particular, PG1404+226 (incidentally, the object showing the smallest 𝑀_BH and the largest deviation with respect to the 𝑀_BH-𝑀_host relation in our sample) shows clear spiral arms in the residuals of the host galaxy model. From local galaxy studies, 𝑀_BH is found to be more sensitive to the properties of the spheroidal stellar component rather than of the whole galaxy. On the other hand, a bulge + disc decomposition is practically impossible with ground-based images of quasar host galaxies at relatively high redshift. Here we attempt a rule-of-thumb correction starting from the Sersic index value. We assume that the bulge-to-total luminosity ratio in the rest-frame 𝑅 band, 𝐵/𝑇, scales with the Sersic index as follows:𝑛𝐵/𝑇=^s−0.5/3.5if𝑛_s1<4,if𝑛_s≥4. (2) This simple analytical form roughly traces the bulk of the 𝐵/𝑇 values for 𝑛_s<4, as found by [75], who performed accurate image deconvolution for ~1 million galaxies from the SDSS. Furthermore, it is consistent with the operative hypothesis that all the galaxies well described by a de Vaucouleurs profile (𝑛_s=4) are bulge dominated (𝐵/𝑇≈1), as assumed in our previous study. The effect of this correction is to move disc-dominated host galaxies towards the left side of Figure 4. In particular, all but one source at 𝑀_bulge<10¹⁰M_⊙ would lie above the local relation. The best fit relation is indeed flatter (0.88±0.18 instead of 1.26±0.29), but still consistent with the linear case. The scatter is also increased (0.53 dex, computed over the whole sample; 0.61 and 0.55 dex in the small 𝑀_BH and small 𝑀_bulge subsets, resp.). We stress that the correction reported in (2) is uncertain, because of the wide range of 𝐵/𝑇 values reported for any given 𝑛_s. However, we remark that any correction for the 𝐵/𝑇 would make the case against a population of under-massive black holes in very massive galaxies even stronger.

A similar argument can be used to evaluate how our results are affected by different assumptions on the star formation history. In our study, we adopted the mass-to-light ratio (𝑀/𝐿) of a single stellar population originated at 𝑧_burst=5 and passively evolving down to 𝑧=0. However, objects with significant disc contaminations are expected to have a younger stellar population than old, passive spheroids. This would imply smaller 𝑀/𝐿, that is, less massive host galaxies for a given observed host luminosity. This would make the case against a quasar population lying below the observed 𝑀_BH-𝑀_host relation even more robust.

6. Conclusions

We measured black hole masses and host galaxy luminosities in a sample of 25 low-redshift (𝑧<0.5) quasars selected to have modest (<10⁹M_⊙) black hole masses.

For each object we inferred stellar masses. This allowed us to significantly expand the sampled range of 𝑀_host and 𝑀_BH for quasars. We found the following.(i)The 𝑀_BH-𝑀_host relation holds over all the 2 dex both in terms of 𝑀_BH and 𝑀_host. The relation has a scatter of 0.44 dex; that is, the sampled parameter space is ~5 times larger.(ii)The slope of the 𝑀_BH-𝑀_host relation in quasars is consistent with unity (in a log-log plane), consistently with what observed in quiescent galaxies.(iii)The scatter of the relation increases by ~0.9 dex at the low-mass end.(iv)After applying a simplistic correction for the disc contribution in objects with low Sersic indexes, the slope of the 𝑀_BH-𝑀_host relation is smaller but still consistent with the linear case.(v)No evidence of a population of quasars with relatively modest 𝑀_BH and very high 𝑀_host values is found.

Further studies at even lower 𝑀_BH masses (≲10⁷M_⊙) and at higher redshift could provide further constraints on the early black hole growth and the nature of the seeds, and to pin down the evolution of the 𝑀_BH-host galaxy relations along the Cosmic Time. This requires extremely high-quality imaging of quasar host galaxies that would become possible with the next generation of ELT and laser assisted AO imagers.

Acknowledgments

R. Decarli acknowledges funding from Germany’s national research center for aeronautics and space (DLR, project FKZ 50 OR 1104), based on observations made with the Nordic Optical Telescope, operated on the island of La Palma jointly by Denmark, Finland, Iceland, Norway, and Sweden, in the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofisica de Canarias. This research has made use of the NASA/IPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration. (Facilities: NOT(NOTCAM) SDSS HST).